Testing symmetry and space-time with atomic clocks

Physicists have once again tested and confirmed the predictions made by Einstein’s theory of special relativity — devised over 100 years ago.

The first principle of Einstein’s Special Theory of Relativity is the hypothesis that the speed of light has the same value for all observers no matter what speed they are moving at. One-hundred years after its inception, following a multitude of experimental tests, it sometimes escapes us just how counter-intuitive this idea actually is.

It may, however, be possible that — according to theoretical models of quantum gravitation — this uniformity of space-time does not apply to all particles. Physicists from the Physikalisch-Technische Bundesanstalt (PTB) and the University of Delaware have now tested this hypothesis with a first long-term comparison of two optical ytterbium clocks — which trap a thousand ytterbium atoms in grids made of laser beams — at the Physikalisch-Technische Bundesanstalt (PTB).

With these clocks — possessing a potential error that amounts to only one second in ten billion years — it should be possible to measure even extremely small deviations of the movement of the electrons in ytterbium. The researchers in question did not detect any change when the clocks were oriented differently in space.

The results are published in the current issue of Nature.

A tunable laser excites an extremely narrow-band resonance in an Yb+ ion of an atomic clock. The electron wave function of the ion’s excited state is marked in yellow. Two ions with wave functions that are oriented at right angles are interrogated by means of laser light with an adjustable frequency shift to measure a possible frequency difference. The whole experimental setup rotates together with the Earth once a day relative to the fixed stars ( Physikalisch-Technische Bundesanstalt (PTB))

This result improves the current limit for testing the space-time symmetry by means of experiments by a factor of 100. In addition to this, it confirms the extremely small systematic measurement uncertainty of the optical ytterbium clocks to be less than 4 × 10E-18.

The idea of the constancy of light was revealed by Michelson and Morley in their eponymous 1887 experiment. With the aid of a rotating interferometer, they compared the speed of light along two optical axes running vertically to each other.

A diagram of the deceptively simple Michaelson and Morley experiment which revealed a truly staggering aspect of nature (Encyclopaedia Britannica)

The result of this experiment, which effectively ruled out the existence of the luminiferous aether — the medium through which light was believed to propagate— evidenced one of the fundamental statements of Einstein’s Special Theory of Relativity — that speed of light is the same in all directions of space.

This lead scientists to question if this symmetry of space also applies to the motion of material particles, or if there any directions along which these particles move faster or more slowly although the energy remains the same? For particles with high energies, for example, theoretical models of quantum gravitation predict a violation of symmetry in Lorenz spacetime— named after Hendrik Antoon Lorentz.

An experiment to solve this issue has been conducted using two atomic clocks — the frequencies of which are each controlled by the resonance frequency of a single Yb+ ion that is stored in a trap.

While the electrons of the Yb+ ions have a spherically symmetric distribution in the ground state, in the excited state they exhibit a distinctly elongated wave function and therefore move mainly along one spatial direction.

The orientation of the wave function is determined by a magnetic field applied inside the clock. The field orientation was chosen to be approximately at right angles in the two clocks. The clocks are firmly mounted in a laboratory and rotate together with the Earth once a day (more exactly: once in 23.9345 hours) relative to the fixed stars.

If the electrons’ speed depended on the orientation in space, this should result in a difference in frequency between the two atomic clocks occurring periodically, together with the Earth’s rotation.

An example of a ytterbium clock at the National Institute of Standards and Technology (NIST)

In order to detect such an effect, the frequencies of the Yb+ clocks were compared for more than 1000 hours. During the experiment, no change between the two clocks was observed for the accessible range of period durations from a few minutes up to 80 hours.

Averaged over the total measuring time, both clocks exhibited a relative frequency deviation of less than 3 × 10E-18. This confirms the combined uncertainty of the clock that had previously been estimated to be 4 × 10E-18. This is an important step in the characterization of optical atomic clocks at this level of accuracy. Only after roughly ten billion years would these clocks potentially deviate from each other by one second.

It also, once again, proves the startling predictions of Einstein’s theories, even after 100 years of testing.

Original research: Christian Sanner, Nils Huntemann, Richard Lange, Christian Tamm, Ekkehard Peik, Marianna S. Safronova, Sergey G. Porsev: Optical clock comparison for Lorentz symmetry testing. Nature (2019)